Error in arima of R: too few non-missing observations - r

Question

I am using arima() and auto.arima() of R to get the prediction of sales. The data is at week level for three years.
my code looks like:
x<-c(1571,1501,895,1335,2306,930,2850,1380,975,1080,990,765,615,585,838,555,1449,615,705,465,165,630,330,825,555,720,615,360,765,1080,825,525,885,507,884,1230,342,615,1161,
1585,723,390,690,993,1025,1515,903,990,1510,1638,1461.67,1082,1075,2315,1014,2140,1572,794,1363,1184,1248,1344,1056,816,720,896,608,624,560,512,304,640,640,704,1072,768,
816,640,272,1168,736,1003,864,658.67,768,841,1727,944,848,432,704,850.67,1205,592,1104,976,629,814,1626,933.33,1100.33,1730,2742,1552,1038,826,1888,1440,1372,824,1824,1392,1424,768,464,
960,320,384,512,478,1488,384,338.67,176,624,464,528,592,288,544,418.67,336,752,400,1232,477.67,416,810.67,1256,1040,823,240,1422,704,718,1193,1541,1008,640,752,
1008,864,1507,4123,2176,899,1717,935)
length_data<-length(x)
length_train<-round(length_data*0.80)
forecast_period<-length_data-length_train
train_data<-x[1:length_train]
train_data<-ts(train_data,frequency=52,start=c(1,1))
validation_data<-x[(length_train+1):length_data]
validation_data<-ts(validation_data,frequency=52,start=c(ceiling((length_train)/52),((length_train)%%52+1)))
arima_output<-auto.arima(train_data) # fit the ARIMA Model
arima_validate <- Arima(x=validation_data,model=arima_output)
Error:
Error in stats::arima(x = x, order = order, seasonal = seasonal, include.mean = include.mean, :
too few non-missing observations
What I am doing wrong?
What does it mean by "too few non-missing observations"? I have searched it now net, but did not get any better explanation.
Thanks for any kind of help!

Answer 1

arima_output is a seasonal ARIMA model:
> arima_output
Series: train_data
ARIMA(1,0,1)(0,1,0)[52]
Arima() then attempts to refit this particular model to validation_data. But to fit a seasonal model to a time series, you need at least one full year of observations, since seasonal ARIMA depends on seasonal differencing.
As an illustration, note that Arima() will happily and without errors refit a time series that is double as long as validation_data:
validation_data <- x[(length_train+1):length_data]
validation_data<-ts(rep(validation_data,2),frequency=52,
start=c(ceiling((length_train)/52),((length_train)%%52+1)))
arima_validate <- Arima(x=validation_data,model=arima_output)
One way of dealing with this would be to force auto.arima() to use a nonseasonal model, by specifying D=0:
validation_data <- x[(length_train+1):length_data]
validation_data<-ts(validation_data,frequency=52,
start=c(ceiling((length_train)/52),((length_train)%%52+1)))
arima_output<-auto.arima(train_data, D=0) # fit the ARIMA Model
arima_validate <- Arima(x=validation_data,model=arima_output)
So this did turn out to be more of a CrossValidated question...

Answer 2

Your chosen model is ARIMA(1,0,1)(0,1,0)[52]. That is, it has a seasonal difference of lag 52. Your validation data has 32 observations. So you cannot take the seasonal differences on the validation data without knowing what the training data is.
One way around this is to fit the model to the full time series, and then extract what you want (presumably residuals from the validation portion).
You can also improve the readability of your code:
x <- ts(x, frequency=52, start=c(1,1))
length_data <- length(x)
length_train <- round(length_data*0.80)
train_data <- ts(head(x, length_train),
frequency=frequency(x), start=start(x))
validation_data <- ts(tail(x, length_data-length_train),
frequency=frequency(x), end=end(x))
library(forecast)
arima_train <- auto.arima(train_data)
arima_full <- Arima(x, model=arima_train)
res <- window(residuals(arima_full), start=start(validation_data))